Subject: Damped Coulomb Potential Matrix Elements

From: Fernando Vila <[email-masked]>
Date: Thu, 4 Mar 1999 16:24:34 -0500 (EST)

Dear Fellows,

   For the past weeks I have been trying to calculate the matrix elements
for a damped Coulomb potential to no avail. The potential has the form:

         erf(a|r-R|)
V(r) =  -------------
            |r-R|

where r and R are position vectors and erf(t) is the error function:

             2       t
erf(t) = -------- int  exp(-x^2) dx.
         PI^(1/2)    0

The matrix elements then are of the form:

                                     erf(a|r-R|) gij
<gi|V|gj> = int gi V(r) gj dr = int ----------------- dr
                                        |r-R|

Here gi are spherical Gaussians and gij is the resulting Gaussian from the
Gaussian Product Theorem.

I have tried using techniques similar to those used for the calculation of
the pure Coulomb potential (based on Fourier or Laplace transforms) but
the usual cancellation is not complete.

Any pointers to papers, books or web pages are welcome.. The complete
solution is also very much welcome.. :-)

Thanks to all in advance, Fer.

*******************************************************************************
Fernando D. Vila       
Department of Chemistry              Voice    (412)624-8691
University of Pittsburgh             Fax      (412)624-8552             
Box 90 Chevron Science Center        E-mail   [email-masked]
Pittsburgh, PA 15260, USA            WWW      http://www.pitt.edu/~fer
*******************************************************************************